Viscoelastic data reduction

Dr. javid Jones provided valuable background information and stimulating discussions on the use of viscoelastic data reduction schemes for various types of materials. 

The inherent difficulty in the measurement of the complex dynamic moduli of viscoelastic materials is emphasized by the results of this paper. The agreement among the shifted modulus data as measured by different systems is limited by several difficulties (1) measurement inaccuracies of the instruments, (2) differences in the data reduction techniques used to apply the time-temperature superposition principle and propagation of shift curve errors and, (3) nonuniformity of the test samples. 

Figure 2. Viscoelastic master curves represented on reduced temperature nomograph. Key solid symbols, modulus values and open symbols, loss tangent values. Insert at upper left shows the shift factor function, aT, used for data reduction.

Data Reduction Procedure. The nomograph lends itself readily to reduction of viscoelastic data and is particularly convenient for computerized procedures. If one selects the proper position for Tq and the interval At between Tq and Ti, T2, etc., then the grid of lines can be used to place the test data in position. 

SUMMARY OF COMPUTATION STEPS IN REDUCTION OF VISCOELASTIC DATA... 

There have been many examples where experimental viscoelastic data, both transient and dynamic, superpose with remarkable precision when reduced to a reference temperature in this manner. In other cases, the reduction is successful only in a restricted zone, and deviations occur in other regions of viscoelastic consistency or of temperature. Some examples of the latter and their interpretation are given in Section F below. 

The MRC cycle calls for a 182°C cure temperature. The effect of cure temperature on residual stress was investigated by curing specimens at four other cure temperatures (171, 165, 160, and 149°C) while holding the dwell time (4 hours) constant. In Figure 8.18 the dimensionless curvature for these specimens is plotted versus the cure temperature. The curvature is reduced as the cure temperature is decreased with significant reduction in curvature obtained for dwell temperatures of 165°C or less. The final curvature as predicted by the viscoelastic process model is overlaid with the experimental data in Figure 8.18 and is shown to capture the trend. 

A modified version of the free-volume theory is used to calculate the viscoelastic scaling factor or the Newtonian viscosity reduction where the fractional free volumes of pure polymer and polymer-SCF mixtures are determined from thermodynamic data and equation-of-state models. The significance of the combined EOS and free-volume theory is that the viscoelastic scaling factor can be predicted accurately without requiring any mixture rheological data. 

The general trend of the data reported in Fig. 8 is suggesting the applicability of an empirical time-temperarnre reduction approach that has been already successfully applied to interpret the viscoelastic namre of crack propagation in polymers [31-36]. Master curves for the yielding and the necking/tearing related parts of the specific essential work of fracmre, both referred to a temperature of 23 °C, are reported in Fig. 9 and 10, respectively. The master curves for the Wg y and Wg jit components, have been obtained by horizontally shifting the data of Fig. 8 to best superposition with respect to the data obtained at 23°C. 

In spite of the often large contribution of secondary filler aggregation effects, measurements of the time-temperature dependence of the linear viscoelastic functions of carbon filled rubbers can be treated by conventional methods applying to unfilled amorphous polymers. Thus time or frequency vs. temperature reductions based on the Williams-Landel-Ferry (WLF) equation (162) are generally successful, although usually some additional scatter in the data is observed with filled rubbers. The constants C and C2 in the WLF equation... 

The data were collected by Brookfield EZ-Yield software as shown in Figs. 8 and 9. The test parameters were as follows Spindle - 72, Immersion - Secondary, Zero Speed - 0.1 rpm. Wait Time - 30 s. Run Speeds - 0.05/0.5 rpm. The tests were carried out to either 105 % or 100 % torque reduction. Those tests carried out to 105 % torque reduction were trimmed down to include only those data points leading to and including the peak value of measured shear stress. The test data were exported as a Microsoft Excel spreadsheet. The data from the spreadsheet were then copied into a template developed by David Moonay to calculate the viscoelastic properties of the material. 

In dynamic mechanical tests, the reduced chain mobility due to the crystalline domains is detected by the shift of the damping peak to higher temperatures, that is, the increase of Tg, as already stated for DSC analyses. In addition, as shown in Figure 9.9, the DMTA evidences an increase of the elastic component of the viscoelastic behavior of the polymer as a significant reduction of the damping peak (data from Ref. 32). 

As an example of bulk viscoelastic behavior, data for a poly(vinyl acetate) of moderately high molecular weight are shown in Fig. 2-9. Measurements by McKinney and Belcher of the storage and loss bulk compliance B and B" at various temperatures and pressures are plotted after reduction to a reference temperature and pressure of 50°C and 1 atm respectively (see Chapter 11). The complex bulk compliance is formally analogous to the complex shear compliance, but the two functions present several marked contrasts. 

From the relations among the viscoelastic functions, it follows that multiplication of any modulus function—(7"(w), G(l), E(t), etc.—by coTq/cT and plotting against war or will combine measurements at various temperatures to give a single composite curve which represents reduction of the data to Tq. Correspondingly, any compliance function multiplied by cT/cqTo can be reduced in a similar manner. Multiplication by the concentration-temperature ratio is often denoted by the subscript p. It should be emphasized that the ratio co/c differs from unity by only a very small amount associated with thermal expansion. 

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